If either were to win, the selection would be historic. Not only has there never been an American pope, but the choice could also open a new front in one of the great American rivalries: Dolan is archbishop of New York and O’Malley, the archbishop of Boston.

“They do it in very different ways, but both are gifted,” said Archbishop Joseph E. Kurtz of ­Louisville, who has worked with both men in the US Conference of Catholic Bishops. “I guess I’m not surprised that their names would circulate.”

On the particulars of Roman Catholic teachings, there is no substantive difference between the two Americans, experts said. But their personal styles project different faces of the church.

“O’Malley corresponds to a certain image of spirituality that people long for: simplicity, humility,” said Boston College theology professor James Weiss, a specialist in church history. “Dolan appeals to a different image of spirituality, as something who is buoyant and optimistic.”

Experts in the Vatican’s subtle politics downplay chances that any US cardinal will be the next pope.

But with no obvious front-runner, Dolan and O’Malley could emerge as potential compromise candidates, if the voting among cardinals drags on without one of the favorites secur­ing the two-thirds support required. The conclave did not decide on a new pope on its opening day Tuesday. Deliberations continue Wednesday.

The two Americans maintain a regular working relationship through the US Conference of Catholic Bishops, Kurtz said. Dolan leads the conference as its president; O’Malley chairs the organization’s Committee on Pro-Life Activities.

“I don’t think they go on ­vacation with each other, but I know from just their inter­actions that there’s great mutual respect,” said Kurtz, the conference’s vice president. “Cardinal Dolan will seek Cardinal O’Malley’s advice, especially now that he’s the chair of the prolife committee. He’s often on conference calls that deal with special issues, and [Dolan] ­always defers to his advice.

“Even though they have very different personalities, they seem to work well together,” said Kurtz.

Of the two, Dolan had the higher national profile before the conclave. He has used his platform as president of the bishop’s conference to argue on national political issues, such as the Obama administration’s require­ment that employer-provided health care cover contraception. The church called the requirement an infringement on religious freedom. Dolan was the subject of a television profile by the CBS “60 Minutes” program in 2011, which focused on his high-wattage personality.

“If the cardinals want, not the energizer bunny, but the energizer bear, then they’d go for Dolan,” said Terrence W. Tilley, chairman of the theology depart­ment at Fordham University. “He has a good, maybe a great public persona, and the PR of the church needs work.”

O’Malley, too, has expressed admiration for Dolan’s optimistic outlook. He told The New York Times last week that he enjoyed sending seminarians to the Pontifical North American College in Rome when Dolan was the school’s rector from 1994 to 2001. “His great joy in being a priest is something I wanted my seminarians to exper­ience,” he said.

Dolan, 63, is also a prolific blogger, who updated his Web page almost to the moment the cardinal’s locked themselves in the Sistine Chapel Tuesday to begin their secret deliberations.

“So far, I’ve been unable to find any Irish brown bread, corned-beef, or whiskey,” Dolan posted last Friday from Rome. The next day he joked, “Let’s hope we get home soon — I’m running out of socks!”

O’Malley also publishes a blog, although not as jocular as Dolan’s. On March 1, he posted photographs from his flight to Rome for the conclave and a photo of himself greeting Pope Benedict XVI.

The selection of a pope is cloaked in extreme secrecy, making it impossible for someone outside the conclave to know what the cardinals will do. But the Italian press has ­included O’Malley among the leading contenders, and he topped a poll of Vatican experts published Saturday in an influential newspaper. He was the favorite of the newspaper’s readers in an online poll.

Betting lines at offshore bookmakers reflect the growing public enthusiasm in Rome for the Boston cardinal, who two weeks ago was listed as a 40-1 longshot at the online gambling site paddypower.com. As more bets were placed on O’Malley, the betting line moved to 10-1, the fifth-best odds among all cardinals, behind heavyweights Angelo Scola of Italy, Odilo Scherer of Brazil, Peter Turkson of Ghana, and Marc Ouellet of Canada.

Dolan was listed at 20-1, a slight improvement from his position two weeks ago.

Experts say Dolan’s direct style and ebullient manner probably work against him in the conclave.

“He does not relate by innuendo, which is the curial style,” Tilley said.

Electing Dolan, former head of the Archdiocese of Milwaukee, could also expose the church to renewed criticism over sexual abuse, said Weiss, due to controversial severance payments the Milwaukee Archdiocese used to persuade suspected abusers to leave the priesthood.

Experts attribute O’Malley’s ascension to the perceived top tier of papal candidates to his modest, unassuming style and his reputation as a fixer who cleaned up after sex abuse scandals in Palm Beach, Fall River, and Boston. A member of the Capuchin religious order, O’Malley, 68, is known for his sandals and simple brown robes. After becoming archbishop of Boston in 2003, he sold the archbishop’s mansion in Brighton and moved to a
rectory in the South End.

“When I think of Cardinal O’Malley, I think of the poor,” said Christopher Ruddy, professor of systematic theology at The Catholic University of America. “And I think of a certain simplicity.”

People close to O’Malley rave about his personal charisma, but many others have found the thoughtful and reserved cardinal difficult to get to know. Unlike Dolan, O’Malley does not seem to enjoy the attention that comes with a high church position. O’Malley once wrote that “being archbishop of Boston is like living in a fishbowl made out of magnifying glass.”

One attribute O’Malley would offer as new head of the Catholic Church, said Weiss, is a willingness to listen.

“Recent popes have been very big on talking; we’ve had plenty of cardinals and popes who talk,” he said. “A lot of cardinals are on record saying they want a pope who listens.”